Joint Entrance Examination

Graduate Aptitude Test in Engineering

Strength of Materials Or Solid Mechanics

Structural Analysis

Construction Material and Management

Reinforced Cement Concrete

Steel Structures

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

Hydrology

Irrigation

Geomatics Engineering Or Surveying

Environmental Engineering

Transportation Engineering

Engineering Mathematics

General Aptitude

1

Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl = 35.5 u)

A

1.46

B

0.46

C

1.64

D

0.64

We know, PV = nRT

n = no. of moles = $${m \over M}$$

So, PV = $${m \over M}RT$$

$$ \Rightarrow $$$$\,\,\,\,$$ P = $${m \over V} \times {{RT} \over M}$$

$$ \Rightarrow $$$$\,\,\,\,$$ P = d $$ \times $$ $${{RT} \over M}$$ [ d = density = $${m \over V}$$ ]

at constant temperature and pressure d $$ \propto $$ M

Now let d_{1} and d_{2} are the density of ammonia and HCl.

$$\therefore\,\,\,\,$$ $${{{d_1}} \over {{d_2}}} = {{{M_{N{H_3}}}} \over {{M_{HCl}}}}$$

$$ \Rightarrow $$ $$\,\,\,\,$$ $${{{d_1}} \over {{d_2}}}$$ = $${{17} \over {36.5}}$$ = 0.46

n = no. of moles = $${m \over M}$$

So, PV = $${m \over M}RT$$

$$ \Rightarrow $$$$\,\,\,\,$$ P = $${m \over V} \times {{RT} \over M}$$

$$ \Rightarrow $$$$\,\,\,\,$$ P = d $$ \times $$ $${{RT} \over M}$$ [ d = density = $${m \over V}$$ ]

at constant temperature and pressure d $$ \propto $$ M

Now let d

$$\therefore\,\,\,\,$$ $${{{d_1}} \over {{d_2}}} = {{{M_{N{H_3}}}} \over {{M_{HCl}}}}$$

$$ \Rightarrow $$ $$\,\,\,\,$$ $${{{d_1}} \over {{d_2}}}$$ = $${{17} \over {36.5}}$$ = 0.46

2

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m^{3} at 1000 K. Given R is the gas constant in JK^{$$-$$1}mol^{$$-$$1}, x is :

A

$${{2R} \over {4 + R}}$$

B

$${{2R} \over {4 - R}}$$

C

$${{4 + R} \over {2R}}$$

D

$${{4 - R} \over {2R}}$$

We know,

PV = nRT

Given,

P = 200 Pa

V = 10 m^{3}

T = 1000 K

n = 0.5 + x

$$ \therefore $$ 200 $$ \times $$ 10 = (0.5 + x) R $$ \times $$ 1000

$$ \Rightarrow $$ 0.5 + x = $${2 \over R}$$

$$ \Rightarrow $$ x = $${2 \over R} - {1 \over 2}$$

$$ \Rightarrow $$ x = $${{4 - R} \over {2R}}$$

PV = nRT

Given,

P = 200 Pa

V = 10 m

T = 1000 K

n = 0.5 + x

$$ \therefore $$ 200 $$ \times $$ 10 = (0.5 + x) R $$ \times $$ 1000

$$ \Rightarrow $$ 0.5 + x = $${2 \over R}$$

$$ \Rightarrow $$ x = $${2 \over R} - {1 \over 2}$$

$$ \Rightarrow $$ x = $${{4 - R} \over {2R}}$$

3

The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the gases for equal number of moles are -

A

2P_{A} = 3P_{B}

B

3P_{A} = 2P_{B}

C

P_{A} = 3P_{B}

D

P_{A} = 2P_{B}

Z = PV/nRT

$$ \Rightarrow $$ P = $${{ZnRT} \over V}$$

at constant T and mol(n),

P $$ \propto $$ $${Z \over V}$$

$$ \Rightarrow $$ $${{{P_A}} \over {{P_B}}} = {{{Z_A}} \over {{Z_A}}} \times {{{V_B}} \over {{V_A}}}$$

= $$\left( {{3 \over 1}} \right) \times \left( {{1 \over 2}} \right)$$ = $${3 \over 2}$$

$$ \therefore $$ 2P_{A} = 3P_{B}

$$ \Rightarrow $$ P = $${{ZnRT} \over V}$$

at constant T and mol(n),

P $$ \propto $$ $${Z \over V}$$

$$ \Rightarrow $$ $${{{P_A}} \over {{P_B}}} = {{{Z_A}} \over {{Z_A}}} \times {{{V_B}} \over {{V_A}}}$$

= $$\left( {{3 \over 1}} \right) \times \left( {{1 \over 2}} \right)$$ = $${3 \over 2}$$

$$ \therefore $$ 2P

4

An open vessel at 27^{o}C is heated until two fifth of the air (assumed as an ideal gas) it has escaped from the vessel assuming that the volume of the vessel remains constant, the temperature at which the vessel has been
heated is -

A

750 K

B

500^{o}C

C

750^{o}C

D

500 K

We know,

PV = nRT

As the vessel is open, so the pressure and volume is constant.

$$ \therefore $$ n_{1} R T_{1} = n_{2} R T_{2}

$$ \Rightarrow $$ n_{1} T_{1} = n_{2} T_{1}

$${2 \over 5}$$th of the air escape from the vessel. So the remaining air is $${3 \over 5}$$ of the total air.

$$ \therefore $$ n $$ \times $$ 300 = $${3 \over 5}$$n $$ \times $$ T_{2}

$$ \Rightarrow $$ T_{2} = 500 K

PV = nRT

As the vessel is open, so the pressure and volume is constant.

$$ \therefore $$ n

$$ \Rightarrow $$ n

$${2 \over 5}$$th of the air escape from the vessel. So the remaining air is $${3 \over 5}$$ of the total air.

$$ \therefore $$ n $$ \times $$ 300 = $${3 \over 5}$$n $$ \times $$ T

$$ \Rightarrow $$ T

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (3) *keyboard_arrow_right*

AIEEE 2003 (1) *keyboard_arrow_right*

AIEEE 2004 (2) *keyboard_arrow_right*

AIEEE 2005 (1) *keyboard_arrow_right*

AIEEE 2010 (1) *keyboard_arrow_right*

AIEEE 2011 (1) *keyboard_arrow_right*

AIEEE 2012 (1) *keyboard_arrow_right*

JEE Main 2013 (Offline) (1) *keyboard_arrow_right*

JEE Main 2014 (Offline) (1) *keyboard_arrow_right*

JEE Main 2016 (Offline) (1) *keyboard_arrow_right*

JEE Main 2016 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2016 (Online) 10th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2017 (Online) 8th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2017 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2018 (Online) 16th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th January Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 12th January Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 12th January Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 9th April Evening Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th April Morning Slot (1) *keyboard_arrow_right*

JEE Main 2019 (Online) 10th April Evening Slot (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 2nd September Morning Slot (1) *keyboard_arrow_right*

JEE Main 2020 (Online) 3rd September Evening Slot (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 26th August Evening Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 27th August Morning Shift (1) *keyboard_arrow_right*

JEE Main 2021 (Online) 31st August Morning Shift (1) *keyboard_arrow_right*

Basics of Organic Chemistry *keyboard_arrow_right*

Hydrocarbons *keyboard_arrow_right*

Haloalkanes and Haloarenes *keyboard_arrow_right*

Alcohols, Phenols and Ethers *keyboard_arrow_right*

Aldehydes, Ketones and Carboxylic Acids *keyboard_arrow_right*

Compounds Containing Nitrogen *keyboard_arrow_right*

Polymers *keyboard_arrow_right*

Biomolecules *keyboard_arrow_right*

Chemistry in Everyday Life *keyboard_arrow_right*

Practical Organic Chemistry *keyboard_arrow_right*

Some Basic Concepts of Chemistry *keyboard_arrow_right*

Structure of Atom *keyboard_arrow_right*

Gaseous State *keyboard_arrow_right*

Colloidal State *keyboard_arrow_right*

Redox Reactions *keyboard_arrow_right*

Thermodynamics *keyboard_arrow_right*

Equilibrium *keyboard_arrow_right*

Solid State & Surface Chemistry *keyboard_arrow_right*

Solutions *keyboard_arrow_right*

Electrochemistry *keyboard_arrow_right*

Chemical Kinetics and Nuclear Chemistry *keyboard_arrow_right*

Periodic Table & Periodicity *keyboard_arrow_right*

Chemical Bonding & Molecular Structure *keyboard_arrow_right*

s-Block Elements *keyboard_arrow_right*

Isolation of Elements *keyboard_arrow_right*

Hydrogen *keyboard_arrow_right*

p-Block Elements *keyboard_arrow_right*

d and f Block Elements *keyboard_arrow_right*

Coordination Compounds *keyboard_arrow_right*

Environmental Chemistry *keyboard_arrow_right*